MEMO 2009 ekipno problem 6

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Dodao/la: arhiva
April 28, 2012
Suppose that ABCD is a cyclic quadrilateral and CD=DA. Points E and F belong to the segments AB and BC respectively, and \angle ADC=2\angle EDF. Segments DK and DM are height and median of triangle DEF, respectively. L is the point symmetric to K with respect to M. Prove that the lines DM and BL are parallel.
Source: Srednjoeuropska matematička olimpijada 2009, ekipno natjecanje, problem 6